Klein paradox and the Dirac-Kronig-Penney model

We analyze the barrier problem and the Kronig-Penney model for Dirac particles, paying attention to the Klein paradox and the nature of the potential. The ambiguities associated with the \ensuremath{\delta}-function limit are examined and the physically reasonable way to include \ensuremath{\delta}-function potentials in the Dirac-Kronig-Penney problem is identified.